Cube with cutout corner
You can use the Boolean Modifier


Add a new cube with Shift+A and doublicate the cube with Shift+D
position the second cube where you want to cut out the main cube


Select the cube you want to cut out
Go to the Modifier tab in the Properties window and choose the Boolean Modifier


Set the Operation to Difference
Choose the 2nd cube in the Object list box
Click Apply (Object Mode)


Delete the 2nd cube.


Note: After applying the Boolean Modifier the mesh could be not suitable for a good topology.